@bangobangbang no, you can use the space-time metric with signature either (-,+,+,+) or (+,-,-,-), physicists tend to use the latter and mathematicians the former, however its down to personal choice, this is a long debated topic
@babashroud for small angles tan^-1(O/A) is approximately equal to just O/A, where O is the opposite side length to the angle and A is the adjacent side length to the angle, for angles less than 17 degrees this is accurate to 2 decimal places, and the smaller the angle gets the more accurate the ...
@bangobangbang no, you can use the space-time metric with signature either (-,+,+,+) or (+,-,-,-), physicists tend to use the latter and mathematicians the former, however its down to personal choice, this is a long debated topic